Date: Mon, 10 Jul 1995 18:22:32 EDT
From: "Randy Nichols, ACA Pres." <75542.1003@compuserve.com>

                      CHINESE CRYPTOGRAPHY
                             Part II


ENCIPHERING

Dr. August suggests that the Four Corner System and the Chinese
Phonetic Alphabet System lend themselves to manual cryptographic
treatment.   His treatment of these two systems is easier to
understand than some military texts on the subject. (16)

Let a message in Chinese be X1, X2, X3.. Xn,  where Xi
represents a character.  The code for Xi is vector union of
three sets, v1, v2, and v3.  v1 is a single digit code for tone
v2 is a four or five digit Four Corner representation code,
and v3 is a 6 digit phonetic code representing 3 phonetic
symbols each by two digits.   (17)


                                3
                           Xj = U  v1         eq 1
                               1-3

This union is called an asymmetric code.

The Four Corner System encodes characters into several generic
shapes.  Each character is broken into four (4) quadrants, and
assigned a digit to the generic shape that best corresponds to
the actual shape.  (18)

The Chinese Phonetic Alphabet is Pinyin with symbols instead of
English letters.  Each symbol corresponds to one of 37 ordered
phonetic sounds.  The 21 initial, 3 medial and 13 finals are a
unique ordered set - a true alphabet. (19)

The strength of encryption of Chinese is dependent on the
specific Chinese encoding character schemes.  Three cases are:

  1).  Phonetic Alphabet Only:  The cipher must include both  a
       transposition (to hide cohesion and positional
       limitations) and a substitution (to hide the frequency
       patterns.)

  2)   Four Corner System: The cipher can be based on ring
       operations [performed on codewords rather than
       characters, either on an individual basis or over the
       whole message; the name comes from the algebraic
       operations involving integers mod 10 or mod 37] which
       super-encipher the encoded text.

  3)   Combination of Methods 1) and 2): A text encoded by a
       combination of both methods will need a cipher employing
       both transposition and substitution.  The transposition
       needs to mix up the symbols within codewords and the
       message itself.  This prevents a bifurcated analysis.
       (20)



CRYPTANALYSIS


A) Phonetic Alphabet:

12.6   7   5.7  4.8     4.2   3.8   3.4    3   2.9 2.8 2.4  2.2
 I     U    D   ENG/E   an/en  SH   X/ZH   J/u  G   O   ao   H


2.1   2           1.9  1.8   1.6    1.4  1.3   1.2  1.1
ang   a/b/ai/B/z   ei   Q    ou/M    ie   L     F    R


0.8   0.7  0.6    0.3  0.1
 t    n/c   ch    k/s   p/el


Initials: sh, d

Medials:  i

Finals:  e, en, eng, in, un, ing, ong


Phi for monalphabetic substitution = 0.051
        (random text = 0.027)


Common Digraphs: ji, ieng, ueng, gu, de, ian, iie, li, ien,
                 qi, xi, uo, izh, zu, shi


Positional Limitations:

       1.  Initials follow a medial or final.
       2.  Finals follow an initial or medial.
       3.  [zh, ch, sh ] do not combine with i or u'.
       4.  [ j, q, x ]  do not combine with  a or e  finals.
       5.  qa, qan  = no but quan, qian, qia = yes
       6.  no double phonetics in a single codeword.
       7.  medials double frequently.
       8.  13 limits on combinations within a codeword.

Approximately 63% of characters require 2 phonetic symbols.
About 1/3 were three long, and about 4% are one symbol.

Tone indicator digits were about 22--23% likely.


B) Four Corner

Digital frequencies:  0  =  .30
                      1  =  .14
                      2  =  .15
                      3  =  .07
                      4  =  .10
                      5  =  .03
                      6  =  .07
                      7  =  .08
                      8  =  .04
                      9  =  .02

Phi value = 0.160 compared to random text value of 0.100

Dr. August presents a table of digraphs. (22)   Combinations
of Xn - Ym  where n= 0-9  and m=0,1,2,3,4,7 showed highest
frequencies of text encoded with 5 digit scheme.

DEPENDENCE

In Chinese there is more dependence between encoding and
enciphering operations than in English.  The choice of the
encoding system influences the type of enciphering operations.
Dr. August provides solved examples of the above systems. (21)

============================================================

(16)  D. A. August, "Cryptography and Exploitation of Chinese
      Manual Cryptosystems - Part II:The Encrypting Problem",
      Cryptologia, Vol XIV, No. 1, August 1990.

(17)  D. A. August, "Cryptography and Exploitation of Chinese
      Manual Cryptosystems - Part I:The Encoding Problem",
      Cryptologia, Vol XIII, No. 4, October 1989.

(18)  IBID, Part I. p287.

(19)  IBID, Part I, p299.

(20)  IBID, Part II, p69.

(21)  IBID, Part II, p73-78.

(22)  IBID, Part II, p72.